@book{Sauvigny, author = {Sauvigny, Friedrich}, title = {Spektraltheorie selbstadjungierter Operatoren im Hilbertraum und elliptischer Differentialoperatoren}, publisher = {Springer Spektrum}, address = {Heidelberg [u.a]}, isbn = {978-3-662-58069-1}, doi = {10.1007/978-3-662-58069-1}, pages = {xi, 259}, language = {de} } @misc{Sauvigny, author = {Sauvigny, Friedrich}, title = {Solution of boundary value problems for surfaces of prescribed mean curvature H (x, y, z) with 1-1 central projection via the continuity method}, series = {Lithuanian mathematical journal}, volume = {58}, journal = {Lithuanian mathematical journal}, number = {3}, issn = {1573-8825}, doi = {10.1007/s10986-018-9399-y}, pages = {320 -- 328}, abstract = {When we consider surfaces of prescribed mean curvature H with a one-to-one orthogonal projection onto a plane, we have to study the nonparametric H-surface equation. Now the H-surfaces with a one-to-one central projection onto a plane lead to an interesting elliptic differential equation, which has been discovered for the case H = 0 already by T. Rad{\´o} in 1932. We establish the uniqueness of the Dirichlet problem for this H-surface equation in central projection and develop an estimate for the maximal deviation of large H-surfaces from their boundary values, resembling an inequality by J. Serrin from 1969. We solve the Dirichlet problem for nonvanishing H with compact support via a nonlinear continuity method. Here we introduce conformal parameters into the surface and study the well-known H-surface system. Then we combine these investigations with a differential equation for its unit normal, which has been developed by the author for variable H in 1982. Furthermore, we construct large H-surfaces bounding extreme contours by an approximation. Here we only provide an overview on the relevant proofs; for the more detailed derivations of our results, we refer the readers to the author's investigations in the Pacific Journal of Mathematics and the Milan Journal of Mathematics.}, language = {en} } @misc{Sauvigny, author = {Sauvigny, Friedrich}, title = {Surfaces of prescribed mean curvature H(x,y,z) with one-to-one central projection onto a plane}, series = {Pacific Journal of Mathematics}, volume = {281}, journal = {Pacific Journal of Mathematics}, number = {2}, issn = {0030-8730}, doi = {10.2140/pjm.2016.281.481}, pages = {481 -- 509}, language = {en} } @book{Kuennemann, author = {K{\"u}nnemann, Andreas}, title = {L{\"o}sbarkeit von Randwertproblemen mittels komplexer Integralgleichungen}, publisher = {Springer Spektrum}, address = {Wiesbaden}, isbn = {978-3-658-13126-5}, pages = {XII, 111}, language = {de} } @misc{Sauvigny, author = {Sauvigny, Friedrich}, title = {Maximum Principle for H-Surfaces in the Unit Cone and Dirichlet's Problem for their Equation in Central Projection}, series = {Milan Journal of Mathematics}, volume = {84}, journal = {Milan Journal of Mathematics}, number = {1}, issn = {1424-9286}, doi = {10.1007/s00032-016-0250-9}, pages = {91 -- 104}, language = {en} } @misc{Sauvigny, author = {Sauvigny, Friedrich}, title = {Multiple solutions for the nonparametric Plateau problem within the Euclidean space Rᴾ of arbitrary dimension}, series = {Calculus of Variations and Partial Differential Equations}, volume = {55}, journal = {Calculus of Variations and Partial Differential Equations}, number = {6, Artikel 140}, issn = {0944-2669}, doi = {10.1007/s00526-016-1087-3}, pages = {1 -- 28}, language = {en} } @book{Sauvigny, author = {Sauvigny, Friedrich}, title = {Analysis : Grundlagen, Differentiation, Integrationstheorie, Differentialgleichungen, Variationsmethoden}, publisher = {Springer Spektrum}, address = {Berlin [u.a.]}, isbn = {978-3-642-41506-7}, pages = {XV, 512 S.}, language = {de} } @incollection{HildebrandtSauvigny, author = {Hildebrandt, Stefan and Sauvigny, Friedrich}, title = {On Plateaus's problem in Riemannian manifolds}, series = {Proceedings of the St. Petersburg mathematical society : advances in mathematical analysis of partial differential equations ; dedicated to the memory of Olga Aleksandrovna Ladyzhenskaya}, booktitle = {Proceedings of the St. Petersburg mathematical society : advances in mathematical analysis of partial differential equations ; dedicated to the memory of Olga Aleksandrovna Ladyzhenskaya}, editor = {Apushkinskaya, Darya and Nazarov, Alexander I.}, publisher = {American Mathematical Soc.}, address = {Providence, RI}, isbn = {978-1-4704-1551-8}, pages = {141 -- 152}, language = {en} } @misc{Sauvigny, author = {Sauvigny, Friedrich}, title = {{\"U}ber das Plateausche Problem f{\"u}r Wendelkurven}, series = {Mathematische Semesterberichte}, volume = {60}, journal = {Mathematische Semesterberichte}, number = {2}, issn = {0720-728X}, pages = {151 -- 183}, language = {de} } @phdthesis{Hilschenz, author = {Hilschenz, Michael}, title = {Ein Integralgleichungszugang zu den Minimalvektoren von Marx und Shiffman}, publisher = {Cuvillier}, address = {G{\"o}ttingen}, isbn = {978-3-95404-509-9}, pages = {147}, language = {de} }